1. General

The European Mathematical Cup (abbr. EMC) is held every year in December in cities all over (but not limited to) Europe. The purpose of the EMC is to prepare high school students for other international competitions and to give them a chance to solve a few, hopefully, nice and challenging problems.

The EMC is an open competition. Therefore, students from non-European countries may participate in the competition as well.

The competition takes place in December, during a 9-day interval which is chosen by the EMC Committee. The competition can be organised on any day of the 9-day interval. The exact date varies by location and is usually chosen to be the most suitable within the given time frame.

The EMC is free and open to all high school students. Any attempt to charge the students for participation in the competition is strongly prohibited and will result in disqualification and a loss of the local organizer status for future editions.

2. Participation

The European Mathematical Cup is organized by the association Young Gifted Mathematicians “Marin Getaldić” from Croatia in coordination with local organizers who are responsible for the competition in their location. Requirements for local organizers are described in Section 3.

Any number of contestants from a single location is allowed to participate, but the following limitations exist:

• A local organisation can have more than 10 contestants per category if they mark the solutions of the surplus of contestants themselves, according to the rules set in Section 3.
• The maximum number of contestants from a single country that can be included in the Official Results list is 20 per category. The surplus of the contestants will be listed only in the Local Results list.

Contestants are eligible to participate in the EMC if they are eligible for the next year’s IMO.

The EMC is divided into two categories: Junior and Senior.

• A student can participate in the Junior category if they are less than 17 years old on the day of writing the contest, and if they haven’t yet participated in the IMO.
• Any student who is eligible to participate in the EMC can participate in the Senior Category.
• Local organizers may set additional criteria for students to participate in the Junior category, in agreement with the Central Jury.

3. Local organizers

Local organizers are the people or organisations organizing the EMC in their city or country. (In particular, local organizers are usually university students or mathematics professors). Their obligations are the following:

• Before the contest, they should inform all the potential contestants about the competition and its regulations. They should choose where and when the contest will be held and make the necessary arrangements.
• To organize the contest. If the contest is being held live (usually in a classroom in a local school or university) they hand the problem sheets to contestants (translated into their language if necessary).  If the contest is not being held live, the contest should be held via a video call; all of the contestants must be on the same call as the local organizer and their desks should be clearly visible (local organizers can ask that it is recorded with multiple cameras and we strongly advise; e.g. both using your laptop webcam and your phone to record your laptop screen).  The organizers should send the (translated, if necessary) problems to the contestants via e-mail a few minutes before the competition starts. The contestants should then print the problems. If they do not have a printer, they should copy the problems on a piece of paper. If the contest cannot be held either live or via a video call, the local organizer must contact us and suggest an alternative way to hold the competition. We ask of the local organizers to ensure that the contestants follow the rules.
• After the contest, the local organizers should collect contestants’ solutions or scans and send them to the EMC Committee. We ask them to attach the translations of those parts of the contestants’ work they consider might be worth marks. The translations should be in English or Croatian language and Latin script; all parts of students’ work which are not translated in this fashion will not be marked.
• We expect to receive the scripts, which are to be marked by the Central Jury, no later than 5 days after the last day of the competition.
• For local organizers who decide to mark all or part of their students’ work, we will provide detailed marking schemes of all solutions known to the Central Jury. We still expect to receive scans of locally marked scripts alongside with the marking done and translations of parts where you awarded points no later than 14 days after the last day of the competition. We ask that all parts of the students’ work which were awarded marks are translated, so the Central Jury can ensure the uniformity of the marking. We encourage the local organizers to mark the problems themselves to make the coordination process easier and faster.

Additionally, we invite local organizers to help us by proposing problems. We intend that all of the problems at the EMC are original (not already seen on the Internet or some other competition), so we invite local organizers to send us problem proposals. The problems not selected for the competition are kept confidential forever. It is allowed to propose problems which are not entirely original, but in such cases, we require the full background of such a problem, including whether it has appeared in another competition.

Additionally, we also invite local organizers to participate in the selection process or central grading of the problems to ensure the whole process runs smoothly and fast.

4. Contest regulations

(The contest regulations are very similar to the IMO contest regulations.)

Each contestant may receive the problems in one or two languages subject to the local organizers.

Each contestant must work independently and submit solutions in their language or English (depending on the local organizers). The duration of the competition for both categories is 4 hours. The contest consists of 4 problems. Each problem is worth 10 points. We ask contestants to write only on one side of a plain A4 paper. It is not allowed to write attempts at different problems on the same sheet. Each paper should contain the student’s name, location, category and the number of the problem. If the contestant used more than one page per problem, the pages should be enumerated.

The only instruments permitted in the contest will be writing and drawing instruments, such as rulers and compasses. In particular, books (with the exceptions of dictionaries if writing in English), papers, tables, calculators, protractors, computers and communication devices are not to be allowed.

The local organizers should do their utmost to ensure that no contestant has any information, direct or indirect, about any of the proposed problems. They must also ensure that all contest problems and solutions are kept strictly confidential until after the entire contest has finished.

6. Coordination and results

For each problem, a contestant will receive an integer score out of a maximum of ten points.

As soon as possible after the contest, local organizers will receive preliminary results. When the preliminary results of the competition are announced, a contestant can appeal to their local organizer. Assuming the local organizer agrees with the objection, they can forward it to the EMC Committee not later than 7 days after receiving preliminary results. In this case, the Committee will reconsider the contestant’s solution and contact the local organizer or the contestant for further clarification if necessary.

When the procedure of raising objections and reconsideration of the awarded marks is finished, the preliminary results become final. They will be published on the official site of EMC and sent to local organizers at most two weeks after the preliminary results have been sent.

7. Prizes, medals and certificates

Some of the contestants are awarded prizes and medals, according to the following rules. We say a contestant is a candidate if there are no more than 5 students from the same country and category with more points. Then, for each category separately, we form a list with 6 of the best candidates from each country (we will call this a cut-list). We then set the prize cut-offs so that approximately half of the contestants from the cut-list win a prize, and the numbers of first, second and third prizes are approximately in the ratio 1:2:3. The top 3 candidates from each category are also awarded medals (via post).

Contestants who aren’t candidates but are among the top 20 in their country are listed in the Official Results list and given a prize they’ve earned. All of the contestants are listed in the Local Results list. Every contestant can request a certificate of participation.

A country’s score is defined, for each category separately, as the sum of scores of contestants from the cut-list. A country’s total score is then the sum of the country’s scores in the two categories.